12n
0331
(K12n
0331
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 10 2 4 12 11 6 8 9
Solving Sequence
2,7
6
3,10
11 1 5 4 8 9 12
c
6
c
2
c
10
c
1
c
5
c
4
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.19705 × 10
30
u
29
+ 3.06307 × 10
30
u
28
+ ··· + 1.34207 × 10
30
b − 3.67175 × 10
31
,
− 3.01996 × 10
31
u
29
+ 7.71851 × 10
31
u
28
+ ··· + 2.28151 × 10
31
a − 8.92737 × 10
32
,
u
30
− 2u
29
+ ··· + 54u + 17i
I
u
2
= h19a
4
u + 83a
4
− 123a
3
u + 119a
3
+ 186a
2
u + 202a
2
− 333au + 145b + 499a − 9u − 253,
a
5
− 2a
4
u + a
4
+ 2a
3
u + 2a
3
− 5a
2
u + 4a
2
+ au − 6a + 1, u
2
+ 1i
I
u
3
= h−u
3
+ 2b + u + 1, −u
3
− 2u
2
+ 2a − 3u − 1, u
4
+ u
3
+ u
2
+ 1i
I
u
4
= h−u
5
+ u
4
− u
3
+ 3u
2
+ b − 2u, −u
4
− u
3
− u
2
+ a + u + 2, u
6
+ 2u
4
− 3u
3
+ u
2
− 3u + 1i
* 4 irreducible components of dim
C
= 0, with total 50 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.20 × 10
30
u
29
+ 3.06 × 10
30
u
28
+ · · · + 1.34 × 10
30
b − 3.67 ×
10
31
, −3.02 × 10
31
u
29
+ 7.72 × 10
31
u
28
+ · · · + 2.28 × 10
31
a − 8.93 ×
10
32
, u
30
− 2u
29
+ · · · + 54u + 17i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
10
=
1.32367u
29
− 3.38307u
28
+ ··· + 56.8890u + 39.1292
0.891947u
29
− 2.28235u
28
+ ··· + 38.3521u + 27.3589
a
11
=
1.81045u
29
− 4.61918u
28
+ ··· + 78.0139u + 53.9806
1.03280u
29
− 2.64107u
28
+ ··· + 44.2541u + 31.8222
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
0.469748u
29
− 1.23844u
28
+ ··· + 19.5553u + 13.1538
1.06033u
29
− 2.72603u
28
+ ··· + 44.9653u + 31.7036
a
4
=
1.53008u
29
− 3.96448u
28
+ ··· + 64.5205u + 44.8574
1.06033u
29
− 2.72603u
28
+ ··· + 44.9653u + 31.7036
a
8
=
−0.960602u
29
+ 2.44978u
28
+ ··· − 40.1263u − 29.7290
0.605372u
29
− 1.56263u
28
+ ··· + 25.5542u + 17.0256
a
9
=
0.804706u
29
− 2.05555u
28
+ ··· + 34.2505u + 23.3776
−0.518550u
29
+ 1.32875u
28
+ ··· − 22.1403u − 15.5691
a
12
=
0.580383u
29
− 1.46053u
28
+ ··· + 25.3284u + 18.2709
0.354478u
29
− 0.902566u
28
+ ··· + 15.0764u + 11.6477
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.31952u
29
+ 6.05662u
28
+ ··· − 101.386u − 62.1980
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 36u
28
+ ··· − 842u + 289
c
2
, c
6
u
30
− 2u
29
+ ··· + 54u + 17
c
3
, c
4
, c
7
u
30
− 2u
29
+ ··· + 134u + 17
c
5
, c
10
u
30
− 2u
29
+ ··· − 16u + 64
c
8
, c
11
, c
12
u
30
+ 4u
29
+ ··· + 35u + 4
c
9
u
30
− 24u
29
+ ··· + 37632u + 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 72y
29
+ ··· − 1286386y + 83521
c
2
, c
6
y
30
+ 36y
28
+ ··· − 842y + 289
c
3
, c
4
, c
7
y
30
+ 48y
29
+ ··· + 1526y + 289
c
5
, c
10
y
30
− 24y
29
+ ··· + 37632y + 4096
c
8
, c
11
, c
12
y
30
− 32y
29
+ ··· − 785y + 16
c
9
y
30
− 44y
29
+ ··· − 830537728y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.829037 + 0.437570I
a = 2.03295 + 0.07010I
b = −0.12264 − 1.43896I
3.48161 − 3.37472I 9.82032 + 5.06127I
u = −0.829037 − 0.437570I
a = 2.03295 − 0.07010I
b = −0.12264 + 1.43896I
3.48161 + 3.37472I 9.82032 − 5.06127I
u = 0.126583 + 0.923400I
a = 0.197805 − 0.967738I
b = −0.642069 + 0.460134I
−1.43679 + 1.72806I −2.66066 − 5.45071I
u = 0.126583 − 0.923400I
a = 0.197805 + 0.967738I
b = −0.642069 − 0.460134I
−1.43679 − 1.72806I −2.66066 + 5.45071I
u = 0.186023 + 1.138800I
a = 0.312069 + 0.834385I
b = 0.489861 − 0.585323I
3.94202 + 3.99509I 4.27681 − 3.33940I
u = 0.186023 − 1.138800I
a = 0.312069 − 0.834385I
b = 0.489861 + 0.585323I
3.94202 − 3.99509I 4.27681 + 3.33940I
u = 0.776216 + 0.200551I
a = −0.122985 + 0.288246I
b = −0.437118 − 1.021360I
5.08101 + 0.72288I 10.46952 − 1.61581I
u = 0.776216 − 0.200551I
a = −0.122985 − 0.288246I
b = −0.437118 + 1.021360I
5.08101 − 0.72288I 10.46952 + 1.61581I
u = −0.100734 + 0.756568I
a = −1.29597 + 1.74435I
b = 1.38516 − 0.30781I
1.052880 − 0.788287I 1.82250 − 2.44795I
u = −0.100734 − 0.756568I
a = −1.29597 − 1.74435I
b = 1.38516 + 0.30781I
1.052880 + 0.788287I 1.82250 + 2.44795I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.405861 + 0.639492I
a = −0.273422 − 0.284148I
b = 0.206163 + 0.373793I
0.05508 + 1.46864I 0.73396 − 4.75961I
u = 0.405861 − 0.639492I
a = −0.273422 + 0.284148I
b = 0.206163 − 0.373793I
0.05508 − 1.46864I 0.73396 + 4.75961I
u = −0.531183 + 0.468483I
a = 0.20768 + 1.54378I
b = −0.307002 + 0.554265I
7.65219 − 5.07226I 12.77738 + 5.27340I
u = −0.531183 − 0.468483I
a = 0.20768 − 1.54378I
b = −0.307002 − 0.554265I
7.65219 + 5.07226I 12.77738 − 5.27340I
u = −0.928021 + 0.930066I
a = 0.284525 + 0.123937I
b = 0.185780 + 0.143992I
7.86055 − 3.38055I 1.34955 + 4.07729I
u = −0.928021 − 0.930066I
a = 0.284525 − 0.123937I
b = 0.185780 − 0.143992I
7.86055 + 3.38055I 1.34955 − 4.07729I
u = −1.128230 + 0.737366I
a = −1.42056 − 0.51782I
b = −0.24507 + 1.51911I
11.39290 − 6.89335I 10.03435 + 4.47976I
u = −1.128230 − 0.737366I
a = −1.42056 + 0.51782I
b = −0.24507 − 1.51911I
11.39290 + 6.89335I 10.03435 − 4.47976I
u = −0.566721 + 0.006749I
a = −1.95664 + 1.43740I
b = 0.389339 + 0.933911I
2.43486 + 1.42637I 9.21244 − 2.51396I
u = −0.566721 − 0.006749I
a = −1.95664 − 1.43740I
b = 0.389339 − 0.933911I
2.43486 − 1.42637I 9.21244 + 2.51396I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.22801 + 1.05643I
a = 1.121090 − 0.442399I
b = 0.00806 + 2.83114I
13.79620 + 0.94673I 9.08350 + 0.I
u = 1.22801 − 1.05643I
a = 1.121090 + 0.442399I
b = 0.00806 − 2.83114I
13.79620 − 0.94673I 9.08350 + 0.I
u = 1.10289 + 1.19850I
a = −1.146390 + 0.819322I
b = −0.38922 − 2.83191I
13.2760 + 7.5606I 8.25231 − 4.41681I
u = 1.10289 − 1.19850I
a = −1.146390 − 0.819322I
b = −0.38922 + 2.83191I
13.2760 − 7.5606I 8.25231 + 4.41681I
u = −1.18793 + 1.15252I
a = −0.518013 − 0.112474I
b = −0.508297 − 0.220564I
15.8822 − 4.3416I 9.48749 + 2.02953I
u = −1.18793 − 1.15252I
a = −0.518013 + 0.112474I
b = −0.508297 + 0.220564I
15.8822 + 4.3416I 9.48749 − 2.02953I
u = 1.00823 + 1.34227I
a = 0.94025 − 1.06187I
b = 0.56557 + 2.56886I
−19.2136 + 12.8082I 9.69103 − 5.43858I
u = 1.00823 − 1.34227I
a = 0.94025 + 1.06187I
b = 0.56557 − 2.56886I
−19.2136 − 12.8082I 9.69103 + 5.43858I
u = 1.43803 + 0.89416I
a = −0.818277 + 0.222471I
b = 0.17149 − 2.49018I
−17.5541 − 4.0475I 10.77450 + 0.I
u = 1.43803 − 0.89416I
a = −0.818277 − 0.222471I
b = 0.17149 + 2.49018I
−17.5541 + 4.0475I 10.77450 + 0.I
7
II.
I
u
2
= h19a
4
u −123a
3
u +· · · + 499a − 253, −2a
4
u + 2a
3
u + · · · − 6a + 1, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−1
a
3
=
u
0
a
10
=
a
−0.131034a
4
u + 0.848276a
3
u + ··· − 3.44138a + 1.74483
a
11
=
−0.131034a
4
u + 0.848276a
3
u + ··· − 1.44138a + 1.74483
−a
a
1
=
−u
u
a
5
=
−0.165517a
4
u + 0.124138a
3
u + ··· − 1.82069a + 1.57241
u
a
4
=
−0.165517a
4
u + 0.124138a
3
u + ··· − 1.82069a + 1.57241
u
a
8
=
0.0137931a
4
u − 0.510345a
3
u + ··· + 0.151724a − 0.131034
−1
a
9
=
0.0689655a
4
u − 0.551724a
3
u + ··· + 2.75862a − 1.65517
0.186207a
4
u + 1.11034a
3
u + ··· − 1.95172a + 1.73103
a
12
=
−0.275862a
4
u + 0.206897a
3
u + ··· − 3.03448a + 1.62069
−0.0620690a
4
u − 0.703448a
3
u + ··· + 1.31724a − 1.91034
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
132
145
a
4
u −
156
145
a
4
+
336
145
a
3
u −
28
145
a
3
−
112
145
a
2
u −
764
145
a
2
+
556
145
au −
288
145
a −
612
145
u +
1356
145
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
4
c
6
, c
7
(u
2
+ 1)
5
c
5
, c
10
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
9
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
11
, c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
10
c
2
, c
3
, c
4
c
6
, c
7
(y + 1)
10
c
5
, c
10
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
8
, c
11
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.645450 + 0.271616I
b = −1.46782 − 0.61073I
0.32910 + 1.53058I 4.51511 − 4.43065I
u = 1.000000I
a = −0.74843 + 1.46044I
b = −0.451726 − 1.004750I
5.87256 − 4.40083I 8.74431 + 3.49859I
u = 1.000000I
a = 0.195404 + 0.003972I
b = 1.004750 + 0.451726I
5.87256 + 4.40083I 8.74431 − 3.49859I
u = 1.000000I
a = 0.21165 − 1.80694I
b = 0.61073 + 1.46782I
0.32910 − 1.53058I 4.51511 + 4.43065I
u = 1.000000I
a = −1.30408 + 2.07090I
b = 1.30408 − 1.30408I
2.40108 5.48114 + 0.I
u = − 1.000000I
a = 0.645450 − 0.271616I
b = −1.46782 + 0.61073I
0.32910 − 1.53058I 4.51511 + 4.43065I
u = − 1.000000I
a = −0.74843 − 1.46044I
b = −0.451726 + 1.004750I
5.87256 + 4.40083I 8.74431 − 3.49859I
u = − 1.000000I
a = 0.195404 − 0.003972I
b = 1.004750 − 0.451726I
5.87256 − 4.40083I 8.74431 + 3.49859I
u = − 1.000000I
a = 0.21165 + 1.80694I
b = 0.61073 − 1.46782I
0.32910 + 1.53058I 4.51511 − 4.43065I
u = − 1.000000I
a = −1.30408 − 2.07090I
b = 1.30408 + 1.30408I
2.40108 5.48114 + 0.I
11
III. I
u
3
= h−u
3
+ 2b + u + 1, −u
3
− 2u
2
+ 2a − 3u − 1, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
10
=
1
2
u
3
+ u
2
+
3
2
u +
1
2
1
2
u
3
−
1
2
u −
1
2
a
11
=
1
2
u
3
+ u
2
+
3
2
u +
1
2
1
2
u
3
−
1
2
u −
1
2
a
1
=
u
3
u
3
+ u
2
+ 1
a
5
=
1
u
2
a
4
=
u
2
+ 1
u
2
a
8
=
−u
3
−u
3
− u
2
− 1
a
9
=
1
2
u
3
+ u
2
+
3
2
u +
1
2
1
2
u
3
−
1
2
u −
1
2
a
12
=
3
2
u
3
+ u
2
+
3
2
u +
1
2
3
2
u
3
+ u
2
−
1
2
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1
4
u
3
−
7
2
u
2
−
23
4
u +
37
4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
5
, c
9
, c
10
u
4
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
(u + 1)
4
c
11
, c
12
(u − 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
5
, c
9
, c
10
y
4
c
8
, c
11
, c
12
(y −1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = 0.38053 + 1.53420I
b = −0.927958 − 0.413327I
1.43393 + 1.41510I 8.73606 − 5.88934I
u = 0.351808 − 0.720342I
a = 0.38053 − 1.53420I
b = −0.927958 + 0.413327I
1.43393 − 1.41510I 8.73606 + 5.88934I
u = −0.851808 + 0.911292I
a = −0.130534 + 0.427872I
b = 0.677958 + 0.157780I
8.43568 − 3.16396I 14.13894 − 0.11292I
u = −0.851808 − 0.911292I
a = −0.130534 − 0.427872I
b = 0.677958 − 0.157780I
8.43568 + 3.16396I 14.13894 + 0.11292I
15
IV. I
u
4
=
h−u
5
+u
4
−u
3
+3u
2
+b−2u, −u
4
−u
3
−u
2
+a+u+2, u
6
+2u
4
−3u
3
+u
2
−3u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
10
=
u
4
+ u
3
+ u
2
− u − 2
u
5
− u
4
+ u
3
− 3u
2
+ 2u
a
11
=
u
4
+ u
2
− 2u − 1
−u
4
− 2u
2
+ 2u
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
−u
u
a
4
=
0
u
a
8
=
1
u
2
a
9
=
2u
3
+ u − 2
2u
5
+ 2u
3
− 2u
2
+ u
a
12
=
u
4
− u
3
+ u
2
− 3u
−u
5
− u
4
− u
3
− u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 4u
5
+ 6u
4
− 3u
3
− 13u
2
− 7u + 1
c
2
, c
3
, c
4
c
6
, c
7
u
6
+ 2u
4
− 3u
3
+ u
2
− 3u + 1
c
5
, c
8
, c
10
c
11
, c
12
(u
2
+ u − 1)
3
c
9
(u
2
− 3u + 1)
3
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 4y
5
+ 34y
4
− 107y
3
+ 139y
2
− 75y + 1
c
2
, c
3
, c
4
c
6
, c
7
y
6
+ 4y
5
+ 6y
4
− 3y
3
− 13y
2
− 7y + 1
c
5
, c
8
, c
10
c
11
, c
12
(y
2
− 3y + 1)
3
c
9
(y
2
− 7y + 1)
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170987 + 1.042930I
a = −1.34137 − 1.68750I
b = 1.43598 + 2.26458I
0.986960 10.0000
u = −0.170987 − 1.042930I
a = −1.34137 + 1.68750I
b = 1.43598 − 2.26458I
0.986960 10.0000
u = 1.13928
a = 1.32215
b = 0.0980714
8.88264 10.0000
u = −0.56964 + 1.40480I
a = 0.265976 + 0.868217I
b = −0.66707 − 1.85736I
8.88264 10.0000
u = −0.56964 − 1.40480I
a = 0.265976 − 0.868217I
b = −0.66707 + 1.85736I
8.88264 10.0000
u = 0.341974
a = −2.17136
b = 0.364102
0.986960 10.0000
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
6
+ 4u
5
+ ··· − 7u + 1)
· (u
30
+ 36u
28
+ ··· − 842u + 289)
c
2
(u
2
+ 1)
5
(u
4
− u
3
+ u
2
+ 1)(u
6
+ 2u
4
− 3u
3
+ u
2
− 3u + 1)
· (u
30
− 2u
29
+ ··· + 54u + 17)
c
3
, c
4
(u
2
+ 1)
5
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
6
+ 2u
4
− 3u
3
+ u
2
− 3u + 1)
· (u
30
− 2u
29
+ ··· + 134u + 17)
c
5
, c
10
u
4
(u
2
+ u − 1)
3
(u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1)
· (u
30
− 2u
29
+ ··· − 16u + 64)
c
6
(u
2
+ 1)
5
(u
4
+ u
3
+ u
2
+ 1)(u
6
+ 2u
4
− 3u
3
+ u
2
− 3u + 1)
· (u
30
− 2u
29
+ ··· + 54u + 17)
c
7
(u
2
+ 1)
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
6
+ 2u
4
− 3u
3
+ u
2
− 3u + 1)
· (u
30
− 2u
29
+ ··· + 134u + 17)
c
8
(u + 1)
4
(u
2
+ u − 1)
3
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· (u
30
+ 4u
29
+ ··· + 35u + 4)
c
9
u
4
(u
2
− 3u + 1)
3
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
· (u
30
− 24u
29
+ ··· + 37632u + 4096)
c
11
, c
12
(u − 1)
4
(u
2
+ u − 1)
3
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
30
+ 4u
29
+ ··· + 35u + 4)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
6
− 4y
5
+ 34y
4
− 107y
3
+ 139y
2
− 75y + 1)
· (y
30
+ 72y
29
+ ··· − 1286386y + 83521)
c
2
, c
6
((y + 1)
10
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
6
+ 4y
5
+ ··· − 7y + 1)
· (y
30
+ 36y
28
+ ··· − 842y + 289)
c
3
, c
4
, c
7
(y + 1)
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
6
+ 4y
5
+ 6y
4
− 3y
3
− 13y
2
− 7y + 1)
· (y
30
+ 48y
29
+ ··· + 1526y + 289)
c
5
, c
10
y
4
(y
2
− 3y + 1)
3
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
· (y
30
− 24y
29
+ ··· + 37632y + 4096)
c
8
, c
11
, c
12
(y −1)
4
(y
2
− 3y + 1)
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
30
− 32y
29
+ ··· − 785y + 16)
c
9
y
4
(y
2
− 7y + 1)
3
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
30
− 44y
29
+ ··· − 830537728y + 16777216)
21
